Introduction:
When two identical conductors are maintained at the same temperature and given a potential difference (p.d), the ratio of their drift velocities can be determined. This ratio is influenced by the properties of the conductors and can be calculated using the concept of electrical conductivity.

Explanation:

1. Drift Velocity:
The drift velocity of charge carriers in a conductor refers to the average velocity at which they move in response to an electric field. It is a result of collisions between the charge carriers and the lattice ions within the conductor.

2. Ohm's Law:
According to Ohm's Law, the current flowing through a conductor is directly proportional to the applied voltage and inversely proportional to the resistance. Mathematically, it can be expressed as:
I = V/R
Where I is the current, V is the potential difference (p.d), and R is the resistance.

3. Electrical Conductivity:
The electrical conductivity (σ) of a material determines its ability to conduct electricity. It is given by the formula:
σ = nqμ
Where n is the number of charge carriers per unit volume, q is the charge on each carrier, and μ is the mobility of the carriers.

4. Relationship between Drift Velocity and Electrical Conductivity:
The drift velocity (vd) of charge carriers can be related to the electrical conductivity (σ) using the formula:
vd = μE
Where E is the electric field strength.

5. Ratio of Drift Velocities:
Given that the conductors are identical and at the same temperature, their electrical conductivities (σ) and mobilities (μ) will be equal. Therefore, the ratio of their drift velocities (vd1/vd2) will be equal to the ratio of their electric field strengths (E1/E2).

6. Ratio of Potential Differences:
The electric field strength (E) can be calculated using the potential difference (V) and the length (L) of the conductor. Since the conductors are identical, their lengths will be the same. Hence, the ratio of their potential differences (V1/V2) will be equal to the ratio of their electric field strengths (E1/E2).

Conclusion:
In conclusion, when two identical conductors maintained at the same temperature are given a potential difference in the ratio of 1:2, the ratio of their drift velocities will also be 1:2. This is because the ratio of their electric field strengths, which determines the drift velocity, is equal to the ratio of their potential differences.